Um grafo é ponderado quando suas arestas possuem um peso. O que significa isso? Bom… Vamos supor que eu queira ir de um lugar pra outro, mas o mais importante pra mim não seja a distância entre eles mas o pedágio que vou ter que pagar para pegar cada aresta (estrada). Nesse caso, o peso de cada aresta seria o custo que eu tenho pra passar pela estrada. O problema então seria calcular o caminho onde eu pago menos (o caminho que tem a menor soma de preços) e não o menor caminho no grafo “não-ponderado” (onde consideramos aresta=1 e nada=0).

Neste grafo, por exemplo, o menor caminho de 1 a 3 não é a aresta 1-3, mas sim a aresta 1-2 e depois a aresta 2-3.

Para representar um grafo ponderado usando a matriz de adjacência, onde antes marcávamos “1″, marcamos o peso que temos de ir de um vértice para o outro e onde marcávamos “0″ marcamos $$\infty{}$$ (infinito)*.

 1 2 3 4 1 $$\infty{}$$ 10 40 $$\infty{}$$ 2 10 $$\infty{}$$ 20 50 3 40 20 $$\infty{}$$ 20 4 $$\infty{}$$ 50 20 $$\infty{}$$

* Na verdade, só fazemos isso porque neste caso iríamos querer o menor caminho e o 0 poderia atrapalhar, porque poderíamos ter um caminho sem pedágio, por exemplo, mas isso sempre depende do caso.

Usando listas de adjacência, podemos representar as ligações de cada vértice com dois vetores (um para dizer a qual ele se liga e outro o peso desta ligação) ou com um vetor de structs como:

struct edge { int destino, peso; };

## 1,231 thoughts on “Grafos Ponderados”

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28. Par experience je puis vous dire que parfois au thÃ©Ã¢tre lorsque nous avons Ã  prononcer certains textes, il y a des zÃ©zitations quant aux liaisons z’Ã  Ã©ffectuer. Le pire est en tragÃ©die classique ou certaines liaisons peuvent s’averer catastrophiques…Ou cela tourne justement aux pataquÃ¨s.

29. since i am still awaiting for my comment to be approved that was my point of my post, no godwin’s law were broken just a historical reference based on similar facts about a process not a personality…

30. Fajnie wyglÄ…dasz, wolÄ™ CiÄ™ w takich "spokojniejszych" zestawieniach . MiÅ‚ego pobytu w Londynie, mam nadziejÄ™, Å¼e posty bÄ™dÄ… siÄ™ czÄ™sto pojawiaÄ‡.

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32. Absolutamente!“LiquidaÃ§Ã£o total”, nÃ£o sÃ£o saldos, nÃ£o sÃ£o promoÃ§Ãµes, estÃ£o efectivamente a submeter o PaÃ­s Ã  liquidaÃ§Ã£o.Ã‰ visÃ­vel. Ã‰ triste…Mas eu nÃ£o vou sem dar luta, e tambÃ©m nÃ£o caio em provocaÃ§Ãµes por muito enraivecido que esteja com os verdadeiros filhos da puta psicopatas e sociopatas.

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36. â€œSo what do you fancy yourself â€“ a referee or a preacher?â€A referee, Cy and thanks for asking.Since we’ve all got ideals that we’d like to convert other people to maybe you’ve taken the position of “referee of the preachers” – and we appreciate it Jack.VN:F [1.9.20_1166]please wait…(1 vote cast)VN:F [1.9.20_1166](from 0 votes)

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40. Es difÃ­cil (imposible) hablar de un pueblo o una cultura sin generalizar.Â¿En quÃ© estÃ¡ de acuerdo?, Â¿En quÃ© no estÃ¡ de acuerdo?.En todo caso yo no querÃ­a enfocarme en el por quÃ© una gringa es mÃ¡s atractiva, sino en el que valorÃ¡semos mucho mÃ¡s a nosotros mismos, que tambiÃ©n tenemos virtudes, eso.

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42. anahi este es el 7 mensaje k te mando los ultimos mensajes k tee mandado no han sido contestados meas dececcionado hadita yo confiaba en ti si no contestas este mensaje ya no volvere a confiar en ti porfavor yo confio en ti y ya no te defendere cuando te critiquen un beso y un abrazo laura

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45. AnoucheK dit :ha tiens, j’avais laissÃ© des traces de attentions diplomatiques avec la NZ au niveau du pseudo.Je ne suis qu’Amour entre les peuples qui pourraient tous se donner la main (en faisant attention au H1N1 quand mÃªme).

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48. The pedal body will need to be replaced every year or two(look uses a metal platform to decrease that wear)This replacement cost should be published at the release.

49. Returns March 11th, 2012   For last week Iâ€™ve been neutral to slightly bearish as written (link) seven days ago. Until Tuesday the market showed a considerable pull-back (2.15%). Though the week

50. deda · giovedÃ¬, 21 giugno 2012, 2:16 pmUn mio commento non Ã¨ passato, non conteneva volgaritÃ  e lo riscrivo, Ã¨ difficile farlo perchÃ¨ sono un istintiva ed era lungo, porcaccia la miseria…e non me lo ricordo…verteva sulla quastione pensioni.